Basic properties
| Modulus: | \(1122\) | |
| Conductor: | \(561\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{561}(71,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1122.bn
\(\chi_{1122}(5,\cdot)\) \(\chi_{1122}(71,\cdot)\) \(\chi_{1122}(113,\cdot)\) \(\chi_{1122}(125,\cdot)\) \(\chi_{1122}(245,\cdot)\) \(\chi_{1122}(269,\cdot)\) \(\chi_{1122}(311,\cdot)\) \(\chi_{1122}(317,\cdot)\) \(\chi_{1122}(335,\cdot)\) \(\chi_{1122}(377,\cdot)\) \(\chi_{1122}(401,\cdot)\) \(\chi_{1122}(449,\cdot)\) \(\chi_{1122}(515,\cdot)\) \(\chi_{1122}(521,\cdot)\) \(\chi_{1122}(533,\cdot)\) \(\chi_{1122}(575,\cdot)\) \(\chi_{1122}(581,\cdot)\) \(\chi_{1122}(641,\cdot)\) \(\chi_{1122}(653,\cdot)\) \(\chi_{1122}(707,\cdot)\) \(\chi_{1122}(719,\cdot)\) \(\chi_{1122}(779,\cdot)\) \(\chi_{1122}(785,\cdot)\) \(\chi_{1122}(839,\cdot)\) \(\chi_{1122}(845,\cdot)\) \(\chi_{1122}(911,\cdot)\) \(\chi_{1122}(929,\cdot)\) \(\chi_{1122}(983,\cdot)\) \(\chi_{1122}(1043,\cdot)\) \(\chi_{1122}(1049,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((749,409,1057)\) → \((-1,e\left(\frac{2}{5}\right),e\left(\frac{1}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 1122 }(71, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{80}\right)\) | \(e\left(\frac{39}{80}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{3}{40}\right)\) | \(e\left(\frac{7}{16}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{77}{80}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{69}{80}\right)\) |